Predictive and Specialized Modeling • Process Screening • Statistical Details for the Process Screening Platform
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Statistical Details for the Process Screening Platform
Scaling Factors for Using Medians to Estimate Sigma
When you select Use Medians instead of Means, sigma is estimated using a scaled median range or median standard deviation. The table below gives the scaling factors, which were obtained using Monte Carlo simulation.
For subgroups of size n drawn from a normal distribution, the following are true:
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The theoretical median of the ranges is approximately d2_Median*σ, where d2_Median is the value corresponding to n.
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The theoretical median of the standard deviations is approximately c4_Median*σ, where c4_Median is the value corresponding to n.
Table 18.1 Scaling Constants for Median Range and Median Standard Deviation 
n
d2_Median
c4_Median
2
0.953
0.675
3
1.588
0.833
4
1.978
0.888
5
2.257
0.917
6
2.471
0.933
7
2.646
0.944
8
2.792
0.952
9
2.915
0.959
10
3.024
0.963
11
3.118
0.967
12
3.208
0.969
13
3.286
0.972
14
3.357
0.975
15
3.422
0.976
16
3.483
0.978
17
3.539
0.979
18
3.590
0.980
19
3.640
0.981
20
3.685
0.982
21
3.731
0.983
22
3.770
0.984
23
3.811
0.984
24
3.846
0.985
25
3.883
0.986

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Help created on 7/12/2018